PBW type bases for quantum cluster algebras

Geometric Representation Theory Seminar

Organizers

Lin Chen, Will Donovan, Penghui Li, Peng Shan, Changjian Su, Wenbin Yan

Speaker

Fan Qin 覃帆 (Beijing Normal University)

Time

Fri., 3:30-4:30 pm, May 30, 2025

Venue

B626, Shuangqing Complex Building A

PBW type bases for quantum cluster algebras

Quantum cluster algebras associated with double Bott-Samelson cells have PBW type bases, which consist of monomials of fundamental variables. By extending them to the infinite rank setting, we recover the cluster structure on the virtual Grothendieck rings of representations of quantum affine algebras (i.e., derived Hall algebras). This allows us to compute the fundamental variables via braid group actions.

About the speaker

覃帆，北京师范大学教授，研究方向是代数和表示论。主要研究丛代数和相关领域的课题，包括丛代数与李理论、组合、几何、拓扑的联系。